A simple explanation for the space-based calculation of lava eruption rates

A simple explanation for the space-based calculation oflava eruption rates

Robert Wright a;*, Stephen Blake b, Andrew J.L. Harris a, David A. Rothery b

a Hawai'i Institute of Geophysics and Planetology, University of Hawai'i, Honolulu, HI, USAb Department of Earth Sciences, The Open University, Milton Keynes, UK

Received 26 February 2001; accepted 5 July 2001

Abstract

Knowing how lava effusion rates vary during basaltic eruptions can be of great significance when trying to providepreliminary forecasts regarding how far lava will flow. However, problems exist in accurately determining effusion ratesusing conventional field-based techniques. To ameliorate this problem Harris et al. [J. Geophys. Res. 102 (1997), 7985^8003; Bull. Volcanol. 59 (1997), 49^64; J. Volcanol. Geotherm. Res. 102 (2000), 237^269] developed a method fordetermining effusion rates using infrared satellite data, and showed how the method could be used to provide realisticestimates of effusion rates, repeatedly during several eruptions at Kilauea (Hawai'i) Krafla (Iceland), Etna andStromboli (Italy). Harris et al. [J. Geophys. Res. 102 (1997), 7985^8003; Bull. Volcanol. 59 (1997), 49^64] indicate thattheir method allows instantaneous lava effusion rates to be determined thermodynamically by equating the amount ofheat lost by an active lava flow (derived from the satellite data) to the amount of heat liberated by the cooling mass oflava. The purpose of this paper is to provide a simpler, alternative explanation. We find that rather than being used tocalculate heat loss, Harris et al. [J. Geophys. Res. 102 (1997), 7985^8003; Bull. Volcanol. 59 (1997), 49^64; J. Volcanol.Geotherm. Res. 102 (2000), 237^269] actually use the satellite data to estimate the area of active lava present within thesatellite's field of view at the movement of data acquisition. Thus, changes in the effusion rates they present can only beproportional to changes in this area. The active flow areas were then multiplied by a constant, the value of which isobtained from a crude approximation of the lava flows heat balance. Crucially, the absolute value of this term fallswithin the range of an empirically derived parameter that was found by Pieri and Baloga [J. Volcanol. Geotherm. Res.30 (1986),29^45] to explain strong linear correlations between eruption rate (i.e. the time-averaged effusion rate) andlava flow area for 34 historic Hawaiian flows. As a result, we find that the method of Harris et al. [J. Geophys. Res. 102(1997), 7985^8003] does not yield instantaneous effusion rates, but instead provides a valid and useful way to estimateaverage effusion rates (i.e. the eruption rate) from measurements of flow area. ß 2001 Elsevier Science B.V. All rightsreserved.

Keywords: lava £ows; eruptions; e¡usion; rates; remote sensing

1. Introduction

Volcanologists have long been concerned withtrying to determine how those properties of a lava£ow that are relatively easy to measure can be

0012-821X / 01 / $ ^ see front matter ß 2001 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 0 1 ) 0 0 4 4 3 - 5

* Corresponding author. Present address: Department ofGeography and Earth Sciences, Brunel University, UxbridgeUB8 3PH, UK. Fax: +44-1985-202317.

E-mail address: [email protected] (R. Wright).

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used to quantify important processes that are not.Speci¢cally, much work has investigated how £owmorphology can be used to infer eruption condi-tions, which in turn can be used to improve ourability to forecast £ow growth. Empirical analysesof lava £ow dimensions indicate that this may bepossible, because correlations between £ow lengthand mean e¡usion rate [5,6], £ow length anderupted volume [7], £ow area and mean e¡usionrate [4], and fractal dimension and surface mor-phology [8], have been demonstrated.

Walker [5] was the ¢rst to suggest that the aver-age rate at which lava is erupted from the ventwas the main factor, after lava composition, thatdetermines how far channeled lava £ows. This isessentially an observation that a high eruptionrate allows lava to extend further before it coolsto a halt than does a low eruption rate. Factorsincluding ground slope, erupted volume, eruptiontemperature, lava composition and the nature ofthe environment into which the lava is eruptedalso in£uence the ¢nal dimensions that a £owattains [7,9,10]. However, Walker's original ¢nd-ing, that eruption rate exerts a fundamental con-trol on the lengths of channel-fed lava £ows, ap-pears to be correct (e.g. [9,11]).

Eruption rate data have several important ap-plications. Timely estimates of eruption rate allowempirical models to provide simple predictionsregarding the maximum potential length a lava£ow may attain [9]. More sophisticated numericalmodels of lava £ows also rely on an estimate oferuption rate to drive their simulations [12,13].Thus, data regarding eruption rates are of greatrelevance to hazard management. Eruption ratedata also have wider volcanological applications.Eruption rate determinations provide insight intothe conditions, such as magma ascent dynamics,under which historic lava £ows were emplaced [3].Eruption rate data also provide a means to con-strain the properties and eruption dynamics ofplanetary lava £ows [14,15].

Estimating lava e¡usion rates in the ¢eld, how-ever, is not easy. As a result of the inaccuracy ofthe measurement process itself, inconsistencies inthe methods used, and their natural variabilityover short time-scales, e¡usion rates are often

poorly constrained. Limits on the number of ¢eldvisits during an eruption can also mean that thesedata are collected infrequently or sometimes notat all. Harris et al. [1] introduced a di¡erent ap-proach. They presented a method by which theamount of heat lost by the active lava £ow surface(determined from remotely sensed radiance data)is used to determine the instantaneous rate ofchange in the volume (i.e. e¡usion rate) of anexpanding lava £ow-¢eld. At this point it is im-portant to de¢ne two terms. 'E¡usion rate' refersto the instantaneous, at-vent £ux of lava. Clearlythis is di¤cult to measure and ¢eld-based 'e¡u-sion rates' estimates are generally averaged overa period of tens of seconds. Wadge [16] de¢nessuch time-averaged e¡usion rates as 'eruptionrates' the ultimate example of which being thedivision of ¢nal £ow volume by eruption dura-tion. The period of time over which averagingmust occur before an e¡usion rate is consideredan eruption rate is unclear and subjective. Wadge[16] refers to qualitative time-scales such as 'themajor part of the eruption' and di¡erent eruption'phases'. In this paper we consider e¡usion ratesto refer to the theoretical ideal of the instantane-ous at-vent lava £ux, while eruption rates refer toany such e¡usion rate averaged over a longer pe-riod of time. It is also important to note that inthis paper the term 'eruption rate' refers to lavaeruption rates, as opposed to 'mass eruptionrates', a term used to describe all material (e.g.lava and pyroclasts) erupted from the vent [17].

A space-based route to calculation of lava e¡u-sion rates is attractive. Satellite data acquisitionsare made frequently and at repeated time intervalsfor even the most inaccessible of eruptions.Although satellite observations of the Earth aresubject to error, these errors are largely system-atic, thus removing the more unpredictable ob-server-error that can a¥ict ground-based e¡usionrate estimates. It is, however, not immediately ob-vious how a measurement of the heat lost from anentire lava £ow surface over a period of 1 s can beused to determine the volume of lava issuing froma vent during the same period of time. The pur-pose of this paper is to provide a plausible expla-nation.

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2. Determining lava e¡usion rates from remotelysensed data: the method of Harris et al. [1]

Citing the work of Pieri and Baloga [4] as thebasis for their approach, Harris et al. [1] calculateinstantaneous e¡usion rates Er (m3 s31) duringthe 1991^1993 eruption of Mount Etna using:

Er � F inst

b �CpvT � P cL� �1�

where Finst is the heat £ux measured from the lava£ow surface (in W), b is lava density (2600 kgm33), and Cp is speci¢c heat capacity (1150 Jkg31 K31). vT is the average temperature dropthroughout the active £ow (equal to the initialeruption temperature, T0 = 1080³C, minus thetemperature at which forward movement ceases,TfV900³C), P is the average mass fraction ofcrystals (0.4^0.5) grown in cooling through vT,and cL is latent heat of crystallisation (2.9U105

J kg31).Using infrared radiance data acquired by the

advanced very high resolution radiometer(AVHRR) to determine Finst, Harris et al. [1]used Eq. 1 to calculate e¡usion rates coincidentwith each cloud-free AVHRR image acquisitionmade during the eruption. AVHRR is £own on-board the NOAA series of satellites. Primarily aweather satellite, its pixels are V1 km2 at nadir,with a revisit period of 12 h. Flying two satellitesat any one time allows data for each point on theglobe to be acquired four times in each 24-h peri-od, twice by day, twice by night. This relativelyhigh revisit period meant that 28 cloud-free ac-quisitions were possible during Etna's 1991^1993eruption.

Given some of our previous discussion, com-parison of individual space-based and ground-based measurements provides little insight intothe method's relative accuracy. However, theeruption rate of 5.6 to 7.6 m3 s31 Harris et al.[1] calculated for the entire 1991^1993 Etna erup-tion bounds the rate of 5.8 m3s31 derived fromglobal positioning system ¢eld measurements of¢nal £ow-¢eld volume [18]. Furthermore, inte-grating the 28 space-based e¡usion rate estimatesover the duration of the eruption gives a ¢nal £ow

volume for the 1991^1993 Etna £ow (220^300U106 m3) that is comparable with ground-based measurements (V235U106 m3 ; [18]). Theirresults are also qualitatively consistent with theclassical waxing and waning e¡usion rate patterntypical of large basaltic eruptions of this kind [16].The same pattern is also apparent in eruptionrates computed for the 1983 and 1999 eruptionsof Mount Etna and the 1980 and 1984 eruptionsof Kra£a, Iceland [3]. Furthermore, the absolutee¡usion rate values they present are realistic whencompared to ¢eld estimates.

Harris et al. [2] state that `è¡usion rates can becalculated by equating (the total heat lost by theactive £ow) with the heat supplied by cooling andcrystallisation of the mass of active lava'' whileHarris et al. [19] state that `è¡usion rate can beestimated if the total thermal £ux for a moving £owis known, (as the total thermal £ux) will equal therate at which heat is transferred into the open £ow-¢eld system by lava £owing into and through it, andthe latent heat of crystallisation''. The implicationof this is that they believe the method provides athermodynamic route to calculating lava e¡usionrates. We now go on to provide an alternativeexplanation.

3. Measuring lava £ow areas as a means todetermining eruption rates

Harris et al. [1] used AVHRR channels 3 and 4(which cover the wavelength intervals 3.55^3.93Wm and 10.50^11.50 Wm, respectively) as a basisfor determining heat £ux from the £ow boundaryto the atmosphere. However, widespread satura-tion of channel 3 (a situation encountered whenthe radiance emitted by the lava £ow exceeds themaximum measurable signal of the detector)meant that surface temperatures could not be de-termined directly from the satellite data. Instead,Harris et al. [1] assumed temperatures of 100³Cand 500³C, and then calculated the area of lavawithin each AVHRR pixel necessary to producethe observed (unsaturated) channel 4 radiance.For a given pixel radiance the area calculated,A, is inversely proportional to the assumed tem-perature (i.e. assuming T = 100³C gives the upper

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R. Wright et al. / Earth and Planetary Science Letters 192 (2001) 223^233 225

£ow area, while T = 500³C gives the lower active£ow area). These end-member temperatures forthe £ow surface were chosen to span the intervalwithin which the true surface temperature wasthought to lie. As a result, the area end-membersthey calculated straddled the true area of active£ows measured in the ¢eld. For example, Harriset al. [1] calculated that on 2 January 1992,AT�500�C V 0.75 km2 and AT�100�C of V6 km2.Field data show that the actual area of active£ows on this data was V2.5 km2 [18].

The method of Harris et al. [1] therefore as-sumes that heat loss per unit area of active £owis constant at all points on the £ow surface and atall times during the eruption (the same end-mem-ber range of T was assumed for each image date).Finst was derived by multiplying this constant heatloss per unit area by the calculated areas. As theonly variable in their analysis is the calculated ac-tive £ow area, Eq. 1 is more accurately written as:

Er � FT

b �CpvT � P cL� AT �2�

where FT is the heat loss per unit area for anassumed surface temperature T (100³C or500³C), and AT is the area of lava at temperatureT needed to generate the observed at-satellite ra-diance. The term that relates Er and AT in Eq. 2 isheld constant by Harris et al. [1] for all eruptiondates analysed. Thus, the variation in Er they re-port is, and can only be, proportional to changesin the lava £ow areas they calculate.

The signi¢cance of this can be viewed in thecontext of empirical results obtained by Pieriand Baloga [4], who analysed 34 lava £ows em-placed during six Hawaiian eruptions and foundthat lava £ow area and eruption rate were linearlyrelated, with correlation coe¤cients of between0.88 and 0.99. Based on a one-dimensional heattransport analysis of a lava £ow advancing untilradiative cooling had brought the lava tempera-ture to some su¤ciently low freezing temperature,they predicted a linear proportionality betweeneruption rate, Q and ¢nal £ow area, A :

Q � OcT4e

bCp�T03T f�A�L� �3�

Here, Q is the eruption rate (averaged over thewhole eruption duration), A(L) is the ¢nal planarea of the lava £ow (attained when it achieves its¢nal length, L), Te is the e¡ective radiation tem-perature of the lava £ow surface, T0 is the lavaeruption temperature, and Tf is the temperatureof the £ow front at the time the £ow has cooled toa halt. To test the validity of this model Pieri andBaloga [4] used measured values of Q and A, andassumed values for T0 and Tf , to see if Eq. 3predicted 'realistic' values for Te, the e¡ective ra-diation temperature of the surface of the £ows (Te

is the arealy weighted temperature of cool surfacecrust and high temperature cracks within thiscrust). Assuming T03Tf = 200³C, b = 2600 kgm33 and Cp = 1150 J kg31 K31, they empiricallydetermined values of Te mostly in the rangeV100^600³C for the group of £ows they ana-lysed, with a couple of values close to 700³C. Pieriand Baloga [4] never actually used Eq. 3 to esti-mate eruption rates, and to do so would havebeen problematic as Te could only be determinedempirically. For example, Pieri and Baloga [4]compared empirically determined values of Te

with ¢eld-based thermal video camera data forone of the £ows included in their data set. How-ever, to force agreement between the Te predictedby Eq. 3 and the ¢eld measurements they had to,unrealistically, assume a lava cessation tempera-ture below the solidus. Thus, it appears that Eq. 3is unsuitable for determining unique values of Qfrom measurements of A. However, using therange of Te that Pieri and Baloga [4] determinedempirically as end-members (in e¡ect treating Eq.3 as an empirical rather than an analytical solu-tion) would allow an envelope of eruption rates tobe determined. Speci¢cally, if A is known andT03Tf = 200³C, b = 2600 kg m33, Cp = 1150 Jkg31 K31, and end-member values of Te = 100³Cand Te = 700³C were assumed, solution of Eq. 3would yield an estimate of Q that should embracethe true value (Fig. 1).

Potentially, a more precise estimation of Qcould be obtained if a judgement could be maderegarding the relative thermal e¤ciency of the£ow in question (i.e. whether to assume a valuecloser to 100³C rather than 700³C when solvingEq. 3). Pieri and Baloga [4] report evidence of

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systematic variations in observed Q :A ratios be-tween channel and tube-fed £ows within the 34£ows they analysed, with channel-fed £ows beingcharacterised by relatively higher ratios. As a re-sult, Te predicted by Eq. 3 was higher for channel-fed (up to 600³C) than tube-fed £ows (up to200³C). This is consistent with the observationthat channel-fed £ows exhibit higher surface tem-peratures, lose heat more quickly, and thereforeattain smaller area for a given eruption rate (i.e.higher Q :A) than do tube-fed £ows [20].

Harris et al. [1] cite the work of Pieri and Ba-loga [4], and speci¢cally Eq. 3, as the basis fortheir method. Comparison of Eq. 2 and Eq. 3reveals that they are virtually identical. When ap-plying Eq. 2, Harris et al. [1] assigned the samevalues for T03Tf (equivalent to vT), b and Cp asPieri and Baloga [4] assumed in their analysis. Therange of surface temperatures (100^500³C) as-sumed by Harris et al. [1] also falls within therange of Te empirically derived (V100^700³C)by Pieri and Baloga [4]. Although Harris et al.[1] include an extra term to describe latent heatwhich Pieri and Baloga [4] do not (PcL ; compareEq. 2 with Eq. 3), this cancels out by virtue of thefact that Harris et al. [1] estimate FT , the heat lost

from the £ow boundary at the assumed temper-atures, as the sum of radiative heat loss and freeconvective heat loss (Pieri and Baloga [4] consid-ered only radiative cooling). Thus, the absolutevalue of the term that relates Er and AT in Eq.2 inevitably falls within the range of that whichPieri and Baloga [4] found to empirically relate Qand A for £ows on Hawai'i.

This conclusion has great signi¢cance in termsof understanding how the method of Harris et al.[1^3] works. Although lava £ow cooling is clearlya controlling factor in determining the relation-ship between eruption rate and the area a lava£ow attains, we do not argue that the physicalmodels presented by Harris et al. [1] or Pieriand Baloga [4] allow this relationship to be quan-ti¢ed robustly, as there are some clear de¢cienciesassociated with both. As previously mentioned,the only way Pieri and Baloga [4] could maketheir model predictions regarding £ow surfacetemperatures match ¢eld data was to assume a£ow cessation temperature that was below thelava solidus. This was due to the fact that theirmodel assumed a £ow covered by an in¢nitelythin surface crust. Harris et al. [1] extend themodel of Pieri and Baloga [4] by including a

Fig. 1. Dashed lines represent eruption rates (Q) calculated using Eq. 3 for various lava £ow areas (A) with surface temperatures(Te) of 100³C, 300³C, 500³C, and 700³C. Symbols depict measured ¢eld values of Q and A for 34 Hawaiian lava £ows (takenfrom ¢gure 1 in [4]).

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term to describe latent heat release. Harris et al.[1] calculate Er assuming latent heat losses over acrystallisation interval of 40^50%. However, as-suming that lava at 1080³C (the eruption temper-ature used by Harris et al. [1,3] for Etna) contains40% crystals on eruption, it will stop £owing longbefore it attains the cessation temperature theyassume. This is because, given additional post-eruption crystallisation of 40%, by the time the£ow reaches the cessation temperature it will con-tain too many crystals to £ow [21,22]. Althoughthe exact amount of crystallisation will vary fromcase to case (Harris et al. [3] provide a descriptionof the e¡ect varying crystal content has on theresults they present), this is in e¡ect equivalentto an overestimation of the heat liberated by thelava £ow. However, in the original work of Harriset al. [1] this does not signi¢cantly a¡ect the ac-curacy of their results because, as previously men-tioned, the inclusion of heat loss terms describingfree convection from the £ow surface essentiallycancels this 'extra' latent heat out. Thus, the valueof the constant by which Q and A are related inthe work of Harris et al. [1] remains virtually thesame as that determined by Pieri and Baloga [4].

Despite these limitations, the method of Harriset al. [1] produces results that are consistentlyrealistic when compared to ¢eld data. We arguethat this success is not the result of detailed char-acterisation of the £ows' thermal budgets, but isinstead attributable to the fact that the constantby which Harris et al. [1] multiply space-basedestimates of lava £ow area is numerically withinthe range of that which Pieri and Baloga [4] foundempirically to explain relationships between Qand A for a suite of Hawaiian £ows.

3.1. Eruption rates versus e¡usion rates

By applying essentially the same empirical rela-tionship derived by Pieri and Baloga [4] the 'e¡u-sion rate' estimates presented by Harris et al. [1]are more precisely termed lava eruption rates, theabsolute value being proportional to the area overwhich lava has managed to spread by the momentof image acquisition. Thus, it is more accurate tosubstitute Q for Er in Eq. 3. This seems sensible,as the area a lava £ow covers within the ¢eld of

view of an Earth-orbiting satellite at-an-instant isnot a function of the instantaneous e¡usion rateat that moment, but is rather a function of theaverage e¡usion rate (i.e. the eruption rate) prev-alent up to that time.

A characteristic of many basaltic eruptions isthat e¡usion rates rise rapidly to a peak soonafter the onset of eruption and then decrease ex-ponentially [16]. Thus, the eruption rate (whencalculated for the entire eruptive episode) will beunrepresentative of the e¡usion rate at most timesduring the eruption (Fig. 2). However, if the erup-tion rate is calculated at regular time intervalsduring an eruption then a histogram of eruptionrates can be compiled that will provide a closerapproximation of how e¡usion rates actually var-ied [16]. By estimating eruption rates 28 times

Fig. 2. Top: Schematic diagram of the variation of magmadischarge during basaltic eruptions described by Wadge [16].Dividing the ¢nal £ow volume by the total duration of theeruption gives an eruption rate which is unrepresentative ofthe instantaneous e¡usion rate at most times during theeruption. Bottom: By calculating eruption rates at severaltime intervals during the eruption, a histogram of eruptionrates approximates how instantaneous e¡usion rates actuallyvaried.

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during the 1991^1993 Etna eruption, Harris et al.[1] do indeed construct such a histogram, explain-ing why their eruption rates show good agreementwith ground-measured e¡usion rates.

3.2. The importance of distinguishing active £owsfrom inactive £ows

When using satellite data to estimate eruptionrates from space at any point during an eruption,it is only the area of those £ows active at themoment of image acquisition that is of any im-portance. The area of older, inactive £ows is of noconsequence as they may have been emplaced atan entirely di¡erent eruption rate. This was rec-ognised by Zimbelman [15] who tried to deter-mine eruption rates of planetary lava £ows byapplying empirical relationships between £owmorphology and eruption rate derived for terres-trial £ows. He concludes that it is necessary toconsider only the dimensions of individual lava£ow units, rather than the combined dimensionsof compound lava £ow-¢elds. This is becausemost empirical relationships, and indeed the rela-tionship between eruption rate and area derivedby Pieri and Baloga [4], are derived for single unit£ows fed by well-de¢ned channels.

The method of Harris et al. [1], as de¢ned inthis paper, works because the infrared satellitedata provide an e¡ective and consistent meansfor discriminating those £ows that are active atthe moment of satellite overpass (i.e. they are stillhot and emit signi¢cant amounts of thermal en-ergy) from those £ows that are inactive (i.e. theyare relatively cold and emit substantially less).

Whereas Pieri and Baloga [4] restricted theiranalysis to single unit lava £ows, the areas calcu-lated by Harris et al. [1] will almost certainly rep-resent the combined areas of many £ows activesimultaneously. Measuring the area of an individ-ual £ow will provide an approximation of theeruption rate that produced it. If such a £ow ismerely one of several £ows active at that time thiswill not describe the total eruption rate. Here, thesynoptic data collection of orbiting satellite sen-sors becomes important. Calculating the area ofall active £ows with the £ow-¢eld is equivalent to

assuming that the sum of their individual areaswas emplaced as a single unit, rather than as sev-eral smaller £ows. Thus, by measuring the totalarea of active £ows, infrared satellite data can beused to approximate the total prevailing eruptionrate.

3.3. Summary

The method of Harris et al. [1] therefore usesinfrared satellite data to estimate active £ow areaand converts these to an estimate of e¡usion rateusing a model that replicates the empirical rela-tionship between eruption rate and ¢nal £ow areaderived by Pieri and Baloga [4]. The proportion-ality between eruption rate and £ow area was rec-ognised by Crisp and Baloga [14] who used amore complex version of Eq. 3 to estimate erup-tion rates of lava £ows on Mars, based on £owarea measurements taken from Viking images,and an assumption that the Martian lava's hadsimilar thermal properties to their terrestrialcounterparts.

From the work of Harris et al. [1^3] it appearsthat when using low spatial resolution data (e.g.AVHRR), and the range of parameter values em-pirically determined by Pieri and Baloga [4], Eq. 3yields a reasonable envelope of eruption rates atEtna, Kra£a, and Stromboli. This implies thatbasaltic £ows on these volcanoes cool to a haltin a similar way to basaltic £ows on Hawai'i.

4. Example: the October 1999 eruption ofMount Etna

During October 1999 sustained strombolian ac-tivity caused lava to ¢ll and, on 17 October, over-£ow the rim of the Bocca Nuova crater, produc-ing lava £ows which extended as far as 5 kmdown Etna's western £ank. This period of e¡usiveactivity ended on 5 November 1999. We haveused Eq. 3 to estimate eruption rates, usingAVHRR data, for three dates during this erup-tion for which ground-based data, determined byscientists of Sistema Poseidon, Nicolosi, are avail-able for comparison. Fig. 3 shows the results for

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28 and 31 October, and 2 November 1999. Ineach case thermal radiance emitted from anoma-lously radiant AVHRR pixels (R4) was calculatedand the area of lava necessary to produce theobserved radiance for a range of temperatures(AT ) determined using:

AT � R43L4�Tb�L4�T�3L4�Tb� �4�

where L4 is the Planck function radiance emittedat 10.7 Wm (the central wavelength of AVHRRband 4) from surface of temperature T (the lava£ow surface) and Tb (the ambient temperature ofground adjacent to the active lava £ow). T wasvaried between 100³C and 1000³C. Tb was deter-mined from the AVHRR data.

These areas are plotted on Fig. 3, and can beseen to decrease as the assumed temperature in-creases. For each AT the eruption rate was calcu-lated using Eq. 3, with FT set to the radiative heatloss from a surface radiating at temperature T

(FT = OcT4). As T increases, eruption rate initiallydecreases (as the calculated active £ow area de-creases), but then begins to increase as the T4

relationship begins to outweigh the decrease inAT .

Assuming upper and lower values of T of100³C and 600³C [4], Eq. 3 yields eruption rateenvelopes of V18^27 m3 s31 (28 October), V5^9m3 s31 (31 October) and V1^2 m3 s31 (2 Novem-ber). These compare with ¢eld-based eruption rateestimates of V28 m3 s31 (27 October), V5 m3

s31 (31 October) and V1 m3 s31 (2 November)(M. Neri, personal communication). The fact thatthey are not in exact agreement is probably oflittle signi¢cance as both will undoubtedly havea certain amount of associated error. Error in¢eld estimates of eruption rate is likely to stemfrom uncertainties in £ow-¢eld thickness, beingderived from measurements of £ow area and ve-locity, multiplied by less reliable estimates of £owthickness. Error in the satellite-based estimateswill stem from a variety of factors. Firstly, the

Fig. 3. Lava £ow areas (AT ) and e¡usion rates (Q) calculated from AVHRR data acquired on 28 and 31 October, and 2 Novem-ber 1999. On each date, the amount of radiance emitted from the lava £ow surface at 10.7 Wm was obtained from the AVHRRdata. Using techniques described in this paper AT (and subsequently Q) were calculated (from Eqs. 4 and 3, respectively) basedon these radiance values for a range of assumed £ow surface temperatures, T. Plot symbols are used only to aid discriminationbetween the di¡erent curves and do not represent discrete data points.

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empirical relationship upon which they are basedis only a best ¢t to a data set which, as Pieri andBaloga [4] demonstrate (Fig. 1), can have a largedegree of scatter. Crisp and Baloga [14] indicatethat signi¢cant scatter in plots of Q versus A canbe caused by variations in the lava core temper-ature and the extent to which this core is exposedto the atmosphere through cracks in the lava'souter crust.

The method is also reliant on the premise thatlava added to the £ow-¢eld has an expression interms of surface £ows. An increase in eruptionrate which was accommodated by £ow in£ationrather than £ow expansion would clearly be invis-ible to an orbiting satellite, and would remainundetected. Intermittent release of lava stored lo-cally within in£ated £ow-¢elds, such as that re-ported to have occurred at Kilauea, Hawai'i byHon et al. [23], would also cause the method tobreak down. In this example, active lava £owscovering several hundred square metres were ob-served even though supply from the summit re-gion had ceased a day earlier. Tube-fed £ows mayalso introduce complications. Calvari and Pinker-ton [24] report that the 1991^1993 Etna lava £ow,which propagated through an extensive tube sys-tem, extended 3 km further than predicted bylengthê¡usion rate relationships developed foropen-channels £ows.

However, despite these limitations, it appearsfrom the work of Harris et al. [1^3,19] and theexample we present here that Eq. 3 can be used toprovide an approximation of eruption rates in amanner that is both qualitatively and quantita-tively consistent with ground-based data. Wehave used Eq. 3 in this worked example to illus-trate how much the method of Harris et al. [1] hasin common with the work of Pieri and Baloga [4].However, it is important to note that the conclu-sion of this paper is that although the term thatequates eruption rate and £ow area in Eq. 3 at-tempts to approximate the thermal budget of the£ows in question, it was in fact empirically para-meterised by Pieri and Baloga [4]. As such, we donot argue that it allows eruption rates to be cal-culated from a detailed analysis of the lava £ows'thermal budgets. Instead we argue that the term

which relates Q and A in Eq. 3, OcT4e /

bCp(T03Tf ), can in fact be viewed as an empiri-cally parameterised constant. As a result, theupper and lower end-member eruption rate esti-mates presented in this section could have beencalculated using Q = 55.111 A and Q = 1.838 A,respectively.

5. Conclusions

Harris et al. [1^3] proposed that instantaneouslava e¡usion rates can be calculated thermody-namically from remotely sensed radiance data.We provide an alternative explanation. The suc-cess of Harris et al. [1^3] can be attributed to thefact that the area a lava £ow attains is related in asystematic way to the eruption rate that conspiredto produce it. We demonstrate how reasonableeruption rate envelopes can be derived from re-motely sensed radiance data based on estimates oflava £ow area, and an empirically parameterisedslope coe¤cient derived by Pieri and Baloga [4] todescribe eruption rateârea relationships for Ha-waiian £ows.

The satellite-derived eruption rate curves pro-duced by Harris et al. [1], and subsequent studiesby Harris et al. [2,3] are qualitatively consistentwith ¢eld observations and theoretical predictionsof how e¡usion rates should vary during basalticeruptions. The quantitative accuracy of the space-based method is harder to determine. However,the absolute eruption rates reported by Harris etal. [1^3] and in this paper are certainly of thecorrect magnitude, and within error of conven-tional ground-based estimates. It is therefore real-istic to conclude that satellite data allow eruptionrates to be estimated, but that they cannot reallybe calculated.

Low spatial resolution (V1 km) remotelysensed radiance data provide an excellent way toestimate active lava £ow areas regularly during aneruption and in a manner that is temporally con-sistent. Such measurements are not limited by theaccessibility of the volcano, or the size of the £ow-¢eld. Currently available data sources includeAVHRR, the along-track scanning radiometer

EPSL 5947 27-9-01


(ATSR [25]), and the recently launched moderateresolution imaging spectro-radiometer (MODIS).ATSR and MODIS both acquire 1-km data in therelevant short-wave infrared wavebands, althoughneither acquire data as frequently as AVHRR(ATSR images the same point on the Earth's sur-face, once by day, once by night, on average everythree days, while MODIS achieves the same tem-poral coverage every 1^2 days). As a result, theintegrated satellite data set acquired by these sen-sors represents a viable means for providingtimely estimates of lava eruption rates at all ofthe Earth's subaeriel volcanoes.

Acknowledgements

We gratefully acknowledge Marco Neri (Siste-ma Poseidon, Sicily) for allowing us to use hisunpublished ¢eld data. RW and AJLH acknowl-edge support from NASA Grant NAG 5-3451awarded to Luke Flynn (HIGP, University of Ha-wai'i). Comments and criticisms provided by Pe-ter Francis (deceased), Dave Pieri, and LionelWilson improved an earlier version of this manu-script. The paper also bene¢ted from formal re-views provided by Laszlo Keszthelyi and an anon-ymous reviewer.[AC]

References

[1] A.J.L. Harris, S. Blake, D.A. Rothery, N.F. Stevens, Achronology of the 1991 to 1993 Etna eruption using ad-vanced very high resolution radiometer data: implicationsfor real-time thermal volcano monitoring, J. Geophys.Res. 102 (1997) 7985^8003.

[2] A.J.L. Harris, A.L. Butterworth, R.W. Carlton, I. Down-ey, P. Miller, P. Navarro, D.A. Rothery, Low-cost volca-no surveillance from space: case studies from Etna, Kra-£a, Cerro Negro, Fogo, Lascar and Erebus, Bull.Volcanol. 59 (1997) 49^64.

[3] A.J.L. Harris, J.B. Murray, S.E. Aries, M.A. Davies, L.P.Flynn, M.J. Wooster, R. Wright, D.A. Rothery, E¡usionrate trends at Etna and Kra£a and their implications foreruptive mechanisms, J. Volcanol. Geotherm. Res. 102(2000) 237^269.

[4] D.C. Pieri, S.M. Baloga, Eruption rate, area, and lengthrelationships for some Hawaiian lava £ows, J. Volcanol.Geotherm. Res. 30 (1986) 29^45.

[5] G.P.L. Walker, Lengths of lava £ows, Phil. Trans. R. Soc.Lond. 274 (1973) 107^118.

[6] H. Pinkerton, L. Wilson, Factors controlling the lengthsof channel-fed lava £ows, Bull. Volcanol. 56 (1994) 108^120.

[7] M.C. Malin, Lenghts of Hawaiian lava £ows, Geology 8(1980) 306^308.

[8] B.C. Bruno, G.J. Taylor, S.K. Rowland, P.G. Lucey, S.Self, Lava £ows are fractals, Geophys. Res. Lett. 19(1992) 305^308.

[9] C.R.J. Kilburn, Lava £ows and £ow ¢elds, in: H. Si-gurdsson, B. Houghton, S. McNutt, H. Rymer, J. Stix(Eds.), Encyclopedia of Volcanoes. Academic Press, Lon-don, 2000, pp. 291^305.

[10] L.P. Keszthelyi, D.C. Pieri, Emplacement of the 75-km-long Carrizozo lava £ow ¢eld, south-central New Mexico,J. Volcanol. Geotherm. Res. 59 (1993) 59^75.

[11] G. Wadge, E¡usion rate and the shape of aa lava £ow-¢elds on Mount Etna, Geology 6 (1978) 503^506.

[12] M. Miyamoto, S. Sasaki, Simulating lava £ows by animproved cellular automata method, Comp. Geosci. 23(1997) 283^292.

[13] A.J.L. Harris, S.K. Rowland, FLOWGO: a kinematicthermo-rheological model for lava £owing in a channel,Bull. Volcanol. 63 (2001) 20^44.

[14] J. Crisp, S. Baloga, A method for estimating eruptionrates of planetary lava £ows, Icarus 85 (1990) 512^515.

[15] J.R. Zimbelman, Emplacement of long lava £ows onplanetary surfaces, J. Geophys. Res. 103 (1998) 27503^27516.

[16] G. Wadge, The variation of magma discharge during ba-saltic eruption, J. Volcanol. Geotherm. Res. 11 (1981)139^168.

[17] H. Sigurdsson, Introduction, in: H. Sigurdsson, B.Houghton, S. McNutt, H. Rymer, J. Stix (Eds.), Encyclo-pedia of Volcanoes. Academic Press, London, 2000,pp. 1^13.

[18] S. Calvari, M. Coltelli, M. Neri, M. Pompilio, V. Soriba-no, The 1991^1993 Etna eruption: Chronology and lava£ow-¢eld evolution, Acta Vulcanol. 4 (1994) 1^14.

[19] A.J.L. Harris, L.P. Flynn, L. Keszthelyi, P.J. Mouginis-Mark, S.K. Rowland, J.A. Resing, Calculation of lavae¡usion rates from Landsat TM data, Bull. Volcanol. 60(1998) 52^71.

[20] L. Keszthelyi, S. Self, Some physical requirements for theemplacement of long basaltic lava £ows, J. Geophys. Res.103 (1998) 27447^27464.

[21] B.D. Marsh, On the crystallinity, probability of occur-rence, and rheology of lava and magma, Contrib. Miner-al. Petrol. 78 (1981) 85^98.

[22] J. Crisp, K.V. Kashman, J.A. Borini, S.B. Hougen, D.C.Pieri, Crystallization history of the 1984 Mauna Loa lava£ow, J. Geophys. Res. 99 (1994) 7177^7198.

[23] K. Hon, J. Kauahikaua, R. Denlinger, K. Mackay, Em-placement and in£ation of pahoehoe sheet £ows: obser-vations and measurements of active lava £ows on Kilauea

EPSL 5947 27-9-01


Volcano, Hawai'i, Geol. Soc. Am. Bull. 106 (1994) 351^370.

[24] S. Calvari, H. Pinkerton, Formation of lava tubes andextensive lava £ow ¢eld during the 1991^1993 eruptionof Mount Etna, J. Geophys. Res. 103 (1998) 27291^27301.

[25] M.J. Wooster, R. Wright, S. Blake, D.A. Rothery, Cool-ing mechanisms and an approximate thermal budget forthe 1991^1993 Mount Etna lava £ow, Geophys. Res. Lett.24 (1997) 3277^3280.

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A simple explanation for the space-based calculation of lava eruption rates